We diffuse a signal (mean curvature) on explicit and implicit surfaces. We use the mesh Laplacian for explicit surface diffusion and the Implicit Closest Point Representation for implicit surface diffusion.
We propose a version of Gaussian for explicit surfaces called the mesh Gaussian. We also extend the method of Gaussian diffusion on implicit surfaces first theorized by Merriman and Ruuth.
ext/ directory contains external libraries I've included for the your convenience
src/ directoy contains support functions used by the main programs
main/ directoy contains the main programs
models/ is empty by design, but will populate as you run programs. It is easier to load saved matrices (e.g. mesh Laplacian), than always constructing them from scratch. models/ directory will build for specific surfaces
- Plane
- Circle
- Sphere
- General Models
You will need a working copy of MATLAB. and gcc 4.7
Only the mesh Laplacian from ext/MeshLP/ needs to be mexed in Matlab. While in Matlab, follow these commands
cd ext/MeshLP/
mexcommands.m
Both the mesh and the cotangent Laplacian will compile. Now your ready to run some example code.
- Andrew Rhodes - Initial Implementation - West Virginia University Ph.D. Student
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Colin Macdonald - Implicit Closest Point Representation at Github
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Jian Sun - mesh Laplacian at Github
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Wil O.C. Ward - icosphere.m
Currently all code is written in MATLAB, though I would like to someday convert it other more open source languages.